Problem: Solve for $x$ and $y$ using elimination. ${4x-6y = -14}$ ${5x-5y = 5}$
Answer: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the top equation by $5$ and the bottom equation by $-6$ ${20x-30y = -70}$ $-30x+30y = -30$ Add the top and bottom equations together. $-10x = -100$ $\dfrac{-10x}{{-10}} = \dfrac{-100}{{-10}}$ ${x = 10}$ Now that you know ${x = 10}$ , plug it back into $\thinspace {4x-6y = -14}\thinspace$ to find $y$ ${4}{(10)}{ - 6y = -14}$ $40-6y = -14$ $40{-40} - 6y = -14{-40}$ $-6y = -54$ $\dfrac{-6y}{{-6}} = \dfrac{-54}{{-6}}$ ${y = 9}$ You can also plug ${x = 10}$ into $\thinspace {5x-5y = 5}\thinspace$ and get the same answer for $y$ : ${5}{(10)}{ - 5y = 5}$ ${y = 9}$